Mastering Physics Solutions Chapter 15 Fluids
Chapter 15 Fluids Q.1CQ
Suppose you drink a liquid through a straw. Explain why the liquid moves upward, against gravity, into your mouth
Solution:
To draw a liquid up a straw, we expand our lungs This reduces the air pressure inside the mouth to less than atmospheric pressure The resulting difference in pressure produces a net upward force on the liquid in the stra4
Chapter 15 Fluids Q.1P
Estimate the weight of the air in your physics classroom.
Solution:
Chapter 15 Fluids Q.2CQ
Considering your answer to the previous question, is it possible to sip liquid througha straw on the surface of the Moon? Explain
Solution:
No. Ibecause the Moon has no atmosphere (of any significance) to press down on the surface of the liguidi
Chapter 15 Fluids Q.2P
What weight of water is required to fill a 25-gallon aquarium?
Solution:
Chapter 15 Fluids Q.3CQ
Water towers on the roofs of buildings have metal bands wrapped around them for support The spacing between bands is smaller near the base of a tower than near its top Explain
Solution:
The pressure in the tank of water increases with depth I The pressure is greatest near the bottom To provide sufficient support there, the metal bands must be spaced more closely together
Chapter 15 Fluids Q.3P
You buy a “gold” ring at a pawn shop. The ring has a mass of 0.014 g and a volume of 0.0022 cm3. Is the ring solid gold,?
Solution:
Chapter 15 Fluids Q.4CQ
What holds a suction cup in place?
Solution:
A suction cup is held in place by atmospheric pressura When the cup is applied, you push it flat against the surface you want to stick it to. This expels most of the air from the cup. and leads to a larger pressure on the outside of the cup IThus. atmospheric pressure pushes the outside of the cup against the surfacel
Chapter 15 Fluids Q.4P
Estimate the weight of a treasure chest filled with gold doubloons.
Solution:
Chapter 15 Fluids Q.5CQ
Solution:
This experiment shows that a certain pressure is needed at the bottom of the water column, and not just a certain weight of water To blow the top off the barrel it is necessary to increase the
pressure in the barrel enough so that the increase in pressure multiplied by the surface area of the top exceeds 400 N. The required height of water provides the necessary increase in
pressure. However the increase in pressure p. g h depends only on the height of the water in the tube, not on its weight.
Chapter 15 Fluids Q.5P
A cube of metal has a mass of 0347 kg and measures 3.21 cm on a side. Calculate the density and identify the metal.
Solution:
Chapter 15 Fluids Q.6CQ
Why is it more practical to use mercury in the barometer shown in Figure 15-4 than water?
Solution:
Chapter 15 Fluids Q.6P
What is the downward force exerted by the abnosphere on a football field, whose dimensions are 360 ft by 160 ft?
Solution:
Chapter 15 Fluids Q.7CQ
An object’s density can be determined by first weighing it in air, then in water (provided the density of the object is greater than the density of water, so that it is totally submerged when placed in water). Explain how these two measurements can give the desired result.
Solution:
Chapter 15 Fluids Q.7P
BIO Bioluminescence Some species of dinoflagellate (a type of unicellular plankton) can produce light as the result of
biochemical reactions within the cell. This light is an example of bioluminescence. It is foundthat bioluminescence in dinofla-gcllates can be triggered by deformation of the cell surface with a pressure as low as one dyne (10−5 N) per square centimeter. What is this pressure in (a) pascals and (b) atmospheres?
Solution:
Chapter 15 Fluids Q.8CQ
How does a balloonist control the vertical motion of a hot-air balloon?
Solution:
The vertical motion of the balloon is controlled by adding and removing of heat to the air in the balloon. The adding and removing of heat causes change the temperature of the air in the balloon Further, the change in temperature will result in change in density of air in the balloon So, one can control the vertical motion of a hot air balloon by controlling the air density in balloon. By adjusting density of the air in balloon we can adjust the elevation and the depression in the vertical motion of the balloon
Chapter 15 Fluids Q.8P
A 79-kg person sits on a 3.7-kg chair. Each leg of the chair makes contact with the floor in a circle that is 1.3 cm in diameter. Find the pressure exerted on the floor by each leg of the chair, assuming the weight is evenly distributed.
Solution:
Chapter 15 Fluids Q.9CQ
Why is ¡t possible forpeople to float without effort inUtah’s Great Salt Lake?
Solution:
The water of this lake has a higher salinity, and thus, a higher density than ocean water In fact. the density of its water is somewhat greater than the density of a typical human bod. This means that a person can float in the salt lake much like a block of wood floats in fresh water
Chapter 15 Fluids Q.9P
To prevent damage to floors (and to increase friction), a crutch will often have a rubber tip attached to its end. If the end of the crutch is a circle of radius 1.2 cm without the tip, and the tip is a circle of radius 2.5 cm, by what factor does the tip reduce the pressure exerted by the crutch?
Solution:
Chapter 15 Fluids Q.10CQ
Physics in the Moviesln the movie Voyage to the Bottom of the Sea, the Earth is experiencing a rapid warming In one scene, large icebergs break up into small, car-size chunks that drop
downward through the water and bounce off the hull of the submarine Seaview. Is this an example of good. bad, or ugly physics? Explain.
Solution:
The physics in this case is pretty ugly Ice floats in water whether it is a house-sized iceberg, a car-sized chunk or a thimble-sized ice cube. ll Earth is warming and icebergs are breaking up into smaller pieces. each of the smaller pieces will be just as buoyant as the original iceberg
Chapter 15 Fluids Q.10P
An inflated basketball has a gauge pressure of 9.9 lb/inz. What is the actual pressure inside the ball?
Solution:
Chapter 15 Fluids Q.11CQ
One day. while snorkeling near the surface of a crystal-clear ocean, it occurs to you that you could go considerably deeper by simply lengthening the snorkel tube. Unfortunately, this does not work well at all Why?
Solution:
The problem is that as you go deeper into the water the pressure pushing against your chest and lungs increases rapidly Even if you had a long tube on your snorkel, you would find it
difficult to expand your lungs to take a breathS The air coming through the snorkel would be at atmosphere pressure. Ibut the water pushing against your chest might have twice that pressura Scuba gear not only holds air for you in a tank, but it also feeds this air to you under pressurel
Chapter 15 Fluids Q.11P
Suppose that when you ride on your 7.70-kgbike the weight of you and the bike is supported equally by the two tires. If the gauge pressure in the tires is 70.5 1b/in and the area of contact between each tire and the road is 7.13 cm2, what is your weight?
Solution:
= 615N
Chapter 15 Fluids Q.12CQ
Since metal is more dense than water, how is it possible for a metal boat to float?
Solution:
The buoyant force exerted on the body is equal to the weight of water displaced by the body. The weight of the fluid also depends on the density of the tluid
Two torces act upon an object when it enters into water torce due to gravity which act directly in the downward direction and an upward buoyance torce which is determined by the weight ot the
water displaced by the objectS An object floats it torce due to gravity is less than the upward buoyance torce In other words, an object floats it its weight is less than the amount ot water it displaces. A metal boat floats because, even though it weighs a lot. it displaces a huge amount ot water that weighs even mora Also, a boat is designed in such a manner so that they it displace sufficient water to assure that it floats easily.
Chapter 15 Fluids Q.12P
IP The weight of your 1420-kg car is supported equally by its four tires, each inflated to a gauge pressure of 35.0 lb/in2. (a) What is the area of contact each tire makes with the road? (b) If the gauge pressure is increased, does the area of contact increase, decrease, or stay the same? (c) What gauge pressure is required to give an area of contact of 116 cm2 for each tire?
Solution:
Chapter 15 Fluids Q.13CQ
A sheet of water passing over a waterfall is thicker near the top than near the bottom Similarly. a stream of water emerging from a water faucet becomes narrower as it falls Explain
Solution:
As the water falls, it speeds up Still, the amount of water that passes a point in a given time is the same at any height. If the thickness of the water stayed the same and its speed increased.
the amount of water per time would increasa IThus, the thickness of the water must decrease to offset the increase in speed
Chapter 15 Fluids Q.13P
CE Two drinking glasses. I and 2. are filled with water to the same depth Glass I has twice the diameter of glass 2. (a) Is the weight of the water in glass 1 greater than, less than, or equal to
the weight of the water in glass 2? (b) Is the pressure at the bottom of glass 1 greater than, less than, or equal to the pressure at the bottom of glass 2?
Solution:
Chapter 15 Fluids Q.14CQ
It is a common observation that smoke rises more rapidly through a chimney when there is a wind blowing outside Lxplain
Solution:
As wind blows across the top of the chimney, a pressure difference is established between the top and the bottom of the chimney. with the top having the lower pressurel This will cause smoke to rise more rapidly
Chapter 15 Fluids Q.14P
Solution:
Chapter 15 Fluids Q.15CQ
Is it best for an airplane to take off against the wind or with the wind? Explain
Solution:
If we take off into the wind, the airspeed over the wings is greater than if we take off with the wind. This means that more lift is produced when taking off into the wind, which is the preferable situ ation
Chapter 15 Fluids Q.15P
Water in the lake behind Hoover Dam is 221 m deep. What is the water pressure at the base of the dam?
Solution:
Chapter 15 Fluids Q.16CQ
If you have a hair dryer and a Ping Pong ball at home. try this demonstration Direct the air from the dryer in a direction just above horizontal Next, place the Ping Pong ball in the stream of air
If done just right, the ball will remain suspended in midair Use the Bernoulli effect to explain this behavior
Solution:
If a ball is placed in a stream of air such that the speed of air over its upper surface is greater than the speed across its lower surface, the result will be a lower pressure at the top of the ball This results in an upward force that can equal the weight of the ball
Chapter 15 Fluids Q.16P
CE Two drinking glasses, 1 and 2, are filled with water to the same depth. Glass 1 has twice the diameter of glass 2. (a) Is the weight of the water in glass 1 greater than, less than, or equal to the weight of the water in glass 2? (b) Is the pressure at the bottom of glass 1 greater than, less than, or equal to the pressure at the bottom of glass 2?
Solution:
Chapter 15 Fluids Q.17CQ
Suppose a pitcher wants to throw a baseball so that it rises as it approaches the batter. How should the ball be spinning to accomplish this feat? Explain.
Solution:
Chapter 15 Fluids Q.17P
As a storm front moves in, you notice that the column of mercury in a barometer rises to only 736 mm. (a) What is the air pressure? (b) If the mercury in this barometer is replaced with water, to what height does the column of water rise? Assume the same air pressure found in part (a).
Solution:
Chapter 15 Fluids Q.18P
Solution:
Chapter 15 Fluids Q.19P
Solution:
Chapter 15 Fluids Q.20P
A cylindrical container witha cross-sectional area of 65.2 cm2 holds a fluid of density 806 kg/m3. At the bottom of the container the pressure is 116 kPa. (a) What is the depth of the fluid? (b) Find the pressure at the bottom of the container after an additional 2.05 × 10−3 m3 of this fluid is added to the container. Assume that no fluid spills o ut of the container.
Solution:
Chapter 15 Fluids Q.21P
IP Tourist Submarine A submarine called the Deep View 66 is currently being developed to take 66 tourists at a time on sightseeing trips to tropical coral reefs. According to guidelines of the AmericanSociety of Mechanical Engineers (ASME), to be safe for human occupancy the Deep View 66 must be able to withstand a pressure of 10.0 N per square millimeter, (a) To what depth can the Deep View 66 safely descend in seawater? (b) If the submarine is used in freshwater instead, is its maximum safe depth greater than, less than, or the same as in seawater? Explain
Solution:
Chapter 15 Fluids Q.22P
Solution:
Chapter 15 Fluids Q.23P
IP You step into an elevator holding a glass of wa ter filled to a depth of 6.9 cm. After a moment, the elevator moves upward with constant acceleration, increasingits speed from 0 to 2.4 m/s in 3.2 s. (a) During the period of acceleration, is the pressure exerted on the bottom of the glass greater than, less than, or the same as before the elevator began to move? Explain, (b) Find the change in the pressure exerted on the bottom of the glass as the elevator accelerates.
Solution:
Chapter 15 Fluids Q.24P
Suppose you pour water into a container until it reaches a depth of 12 cm. Next, you carefully pour ina 7,2-cm thickness of olive oil so that it floats on top of the water. What is the pressure at the bottom of the container?
Solution:
Chapter 15 Fluids Q.25P
Referring to Example 15%, suppose that some vegetable oil has been added to both sides of the U tube. On the right side of the tube, the depth of oil is 5.00 cm, as before. On the left side of the tube, the depth of the oil is 3.00 cm. Find the difference in fluid level between the two sides of the tube.
Solution:
Chapter 15 Fluids Q.26P
P As a stunt, you want to sip some water through a very long, vertical straw, (a) First, explain why the liquid moves upward, against gravity, into your mouth when you sip. (b) What is the tallest straw that you could, in principle, drink from in this way?
Solution:
Chapter 15 Fluids Q.27P
Solution:
Chapter 15 Fluids Q.28P
Acylindrical container 1.0 m tall contains mercury to a certain depth, d. The rest of the cylinder is filled with water, If the pressure at the bottom of the cylinder is two atmospheres, what is the depth d?
Solution:
Chapter 15 Fluids Q.29P
CE Predict/Explain Beebe and BartonOn Wednesday, August 15,1934, William Beebe and Otis Barton made history by descending in the Bathysphere—basically a steel sphere 4.75 ft in diameter—3028 ft below the surface of the ocean, deeper than anyone had been before, (a) As the Bathysphere was lowered, was the buoyant force exerted on it at a depth of 10 ft greater than, less than, or equal to the buoyant force exerted on it at a depth of 50 ft? (b) Choose the best explanation from among the following:
I. The buoyant force depends on the density of the water, which is essentially the same at 10 ft and 50 ft.
II. The pressure increases with depth, and this increases the buoyant force.
III. The buoyant force decreases as an object sinks below the surface of the water.
Solution:
Chapter 15 Fluids Q.30P
CE Lead is more dense than aluminum, (a) Is the buoyant force on a solid lead sphere greater than, less than, or equal to the buoyant force on a solid aluminum sphere of the same diameter? (b) Does your answer to part (a) depend on the fluid that is causing the buoyant force?
Solution:
Chapter 15 Fluids Q.31P
CE A fish canying a pebble in its mouth swims with a small, constant velocity in a small bowl. When the fish drops the pebble to the bottom of the bowl, does the water level rise, fall, or stay the same?
Solution:
The fluid exerts an upward force when an object is placed in that fluid. This force comes from the pressure imposed by the fluid on that particular object.
As the pressure increases, the depth also increases. It depends on the buoyant t say whether the object floats or sinks.
Fish displaces some volume of water, which to become neutrally buoyant. When a fish holds a pebble, water is displaced which is equal to its weight and the weight of the pebble.
Fish adjusts its swim bladder to attain neutral buoyancy, when it drops a pebble into the water. During this activity, the fish displaces water equal to its weight only and the pebble displaces water equal only to its own volume. When the fish drops the pebble, smaller volume of water was displaced concluding that the level of water will fall.
Therefore, the water level will fall.
Chapter 15 Fluids Q.32P
A raft is 4.2 m wide and 6.5 m long. When a horse is loaded fonto the raft, it sinks 2,7 cm deeper into the water. What is the weight of the horse?
Solution:
Chapter 15 Fluids Q.33P
To walk on water, all you need is a pair of water-walking boots shaped like boats. If each boot is 27 cm high and 34 cm wide, how long must they be to support a 75-kg person?
Solution:
Chapter 15 Fluids Q.34P
A3.2-kg balloon is filled with helium (density = 0.179 kg/m3). If the balloon is a sphere with a radius of 4.9 m, what is the maximum weight it can lift?
Solution:
Chapter 15 Fluids Q.35P
A hot-air balloon plus cargo has a mass of 1890 kg and a volume of 11,430 m3. The balloon is floating at a constant height of 6.25 m above the ground, What is the density of the hot air in the balloon?
Solution:
Chapter 15 Fluids Q.36P
In the lab you place a beaker that is half full of water (density pw)on a scale. You now use a high t string to suspend a piece of metal of volume v in the water, The metal is completely submerged, and none of the water spills out of the beaker. Give a symbolic expression for the change in reading of the scale.
Solution:
Chapter 15 Fluids Q.37P
· CE Predict/Explain A block of wood has a steel ball glued one surface. The block can be Floated with the ball “high dry” on its top surface, (a) When the block is inverted, and th ball is immersed in water, does the volume of wood that is submerged increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. When the block is inverted the ball pulls it downward causing more of the block to be submerged.
II. The same amount of mass is supported in either case, there fore the amount of the block that is submerged is the same
III. When the block is inverted the ball experiences a buoyant force, which reduces the buoyant force that must be provided by the wood.
Solution:
Reasoning:
Archimedes principle states that, an object completely immersed in a fluid experience an upward buoyant force equal in magnitude to the weight of fluid displaced by the object. An object floats when it displaces an amount of fluid equal to its weight.
Solution:
(a) If block is inverted, and ball is immersed in the water, the buoyant force experienced
by the steel ball is greater than the buoyant force experienced by the wood block as displaced volume of the water is greater for steel ball than wood block. This result, volume of the wood block that submersed in the water will. Because, buoyant force directly proportional to weight of the displaced volume of the water
(b) When the block is inverted the ball experiences a buoyant force, which reduces the buoyant force that must be provided by the block of wood.
Best explanation is: statement
Chapter 15 Fluids Q.38P
· CE Predict/Explain In the preceding problem, suppose the block of wood with the ball “high and dry” is floating in a tank of water, (a) When the block is inverted, does the water level in the tank increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. Inverting the block makes the block float higher in the water, which lowers the water level in the tank.
II. The same mass is supported by the water in either case, and therefore the amount of displaced water is the same.
III. The inverted block floats lower in the water, which displaces more water and raises the level in the tank.
Solution:
(a)
The weight of the block will be same, whether it is erect or inverted. So the same mass will be supported by the water and thus the volume of water that must be displaced to float the block will be same when it is inverted. As a result, the water level in the tank remains the same.
(b)
The weight of the block will be same, whether it is erect or inverted. So the same mass will be supported by the water and thus the volume of water that must be displaced to float the block will be same when it is inverted. As a result the water level in the tank remains the same. Hence, the best explanation is (II).
Chapter 15 Fluids Q.39P
Solution:
Chapter 15 Fluids Q.40P
CE Predict/Explain Referring to Active Example 15-1, suppose the flask with the wood tied to the bottom is placed on a scale. At some point the string breaks and the wood rises to the surface where it floats, (a) When the wood is floating, is the reading on the scale greater than, less than, or equal to its previous reading? (b) Choose the best explanation from among the following:
I. The same mass is supported by the scale before and after the string breaks, and therefore the reading on the scale remains the same.
II. When the block is floating the water level drops, and this reduces the reading on the scale.
III. When the block is floating it no longer pulls upward on the flask; therefore, the reading on the scale increases.
Solution:
Chapter 15 Fluids Q.41P
CE On a planet in a different solar system the acceleration of gravity is greater than it is on Earth. Tf you float in a pool of water on this planet, do you float higher than, lower than, or at the same level as when you float in water on Earth?
Solution:
As far as floating goes, the planet and Earth are the. This is because gravity has no effect on the equilibrium of a floating body, as the weight and up-thrust will both change by the same factor.
Chapter 15 Fluids Q.42P
An air mattress is 2.3 m long, 0,66 m wide, and 14 cm deep. If the air mattress itself has a mass of 0.22 kg, what is the maximum mass it can support in freshwater?
Solution:
Chapter 15 Fluids Q.43P
A solid block is attached to a spring scale. When the block is suspended in air, the scale reads 20.0 N; when it is completely immeresed in water, the scale reads 17.7 N. What are (a) the volume and (b) the density of the block?
Solution:
Chapter 15 Fluids Q.44P
As in the previous problem, a solid block is suspended from a spring scale. If the reading on the scale when the block is completely immersed in water is 25.0 N, and the reading when it is completly immersed in alcohol of density 806 kg/m3 is 25.7 N, what are (a) the block’s volume and (b) its density?
Solution:
Chapter 15 Fluids Q.45P
BIO Aperson weighs 756 N in air and has abody-fat percentage of 28.1%. (a) What is the overall density of this person’s body? (b) What is the volume of this person’s body? (c) Find the apparent weight of this person when completely submerged in water.
Solution:
Chapter 15 Fluids Q.46P
IP A log floats in a river with one-fourth of its volume above the water, (a) What is the density of the log? (b) If the river carries the log into the ocean, does the portion of the log above the water increase, decrease, or stay the same? Explain.
Solution:
Chapter 15 Fluids Q.47P
A person with a mass of 81 kg and a volume of 0.089 m3 floats quietly in water, (a) What is the volume of the person that is above water? (b) If an upward force F is applied to the person by a friend, the volume of the person above water increases by 0.0018 m3. Find the force F.
Solution:
Chapter 15 Fluids Q.48P
Solution:
Chapter 15 Fluids Q.49P
Apiece of lead has the shape of a hockey puck, with a diameter of 7.5 cm and a height of 2.5 cm. If the puck is placed in a mercury bath, it floats. How deep below the surface of the mercury is the bottom of the lead puck?
Solution:
Chapter 15 Fluids Q.50P
lead weight with a volume of 0.82 × 10−5 m3 is lowered on a fishing line into a lake to a depth of 1.0 m. (a) What tension is required in the fishing line to give the weight an upward acceleration of 2.1 m/s2? (b) If the initial depth of the weight is increased to 2.0 m, does the tension found in part (a) increase, decrease, or stay the same? Explain, (c) What acceleration will the weight have ifthe tension in the fishing line is 1.2 N? Give both direction and magnitude.
Solution:
Chapter 15 Fluids Q.51P
To water the yard, you use a hose with a diameter of 3.4 cm. water flows from the hose with a speed of 1.1 rn/s. If you partially block the end of the hose so the effective diameter is now 0-57 cm, with what speed does water spray from the hose?
Solution:
Chapter 15 Fluids Q.52P
Water flows through a pipe with a speed of 2.1 m/s. Find the flow rate in kg/s if the diameter of the pipe is 3.8 cm.
Solution:
Chapter 15 Fluids Q.53P
To fill a child’s inflatable wading pool, you use a garden hose with a diameter of 2.9 cm. Water flows from this hose with a speed of 1.3 m/s. How long will it take to fill the pool to a depth of 26 cm if the pool is circular and has a diameter of 2.0 m?
Solution:
Chapter 15 Fluids Q.54P
BIO Heart Pump Rate When at rest, your heart pumps blood at the rate of 5.00 liters per minute (L/min). What are the volume and mass of blood pumped by your heart in one day?
Solution:
Chapter 15 Fluids Q.55P
BIO Blood Speed in an Arteriole A typical arteriole has a diameter of 0.030 mm and carries blood at the rate of 5.5 × 10−6 cm3/s. (a) What is the speed of the blood in an arteriole? (b) Suppose an arteriole branches into 340 capillaries, each with a diameter of 4.0 × 10−6 m. What is the blood speed in the capillaries? (The low speed in capillaries is beneficial; it promotes the diffusion of materials to and from the blood.)
Solution:
=0.13cm/s
Chapter 15 Fluids Q.56P
IP Water flows at the rate of 3.11 kg/s through a hose with a diameter of 3.22 cm. (a) What is the speed of water in this hose? (b) If the hose is attached to a nozzle with a diameter of 0.732 cm, what is the speed of water in the nozzle? (c) Is the number of kilograms per second flowing through the nozzle greater than, less than, or equal to 3.11 kg/s? Explain.
Solution:
Chapter 15 Fluids Q.57P
A river narrows at a rapids from a wid th of 12 m to a width of only 5.8 m. The depth of the river before the rapids is 2.7 m; the depth in the rapids is 0.85 m. Find the speed of water flowing in the rapids, given that its speed before the rapids is 1.2 m/s. Assume the river has a rectangular cross section.
Solution:
Chapter 15 Fluids Q.58P
BIO HowMany Capillaries? The aorta has an inside diameter of approximately 2,1 cm, compared to that of a capillary, which is about 1.0 × 10−5 m (10 μm). In addition, the average speed of How is approximately 1.0 m/s in the aorta and 1.0 cm/s in a capillary. Assuming that all the blood that flows through the aorta also flows through the capillaries, how many capillaries does the circulatory system have?
Solution:
Chapter 15 Fluids Q.59P
BIO Plaquein an Artery The buildup of plaque on the walls of an artery may decrease its diameter from 1.1 cm to 0.75 cm. If the speed of blood flow was 15 cm/s before reaching the region of plaque buildup, find (a) the speed of blood flow and (b) the pressure drop within the plaque region.
Solution:
Chapter 15 Fluids Q.60P
A horizontal pipe contains water at a pressure of 110 kPa flowing with a speed of 1.6 m/s. When the pipe narrows to one-half its original diameter, what are (a) the speed and (b) the pressure of the water?
Solution:
Chapter 15 Fluids Q.61P
Solution:
Chapter 15 Fluids Q.62P
IP Water flows through a horizontal tube of diameter 2.8 cm that is joined to a second horizontal tube of diameter 1.6 cm. The pressure difference between the tubes is 7.5 kPa. (a) Which tube has the higher pressure? (b) Which tube has the higher speed of flow? {c) Find the speed of flow in the first tube.
Solution:
Chapter 15 Fluids Q.63P
A garden hose is attached to a water faucet on one end and a spray nozzle on the other end. The water faucet is turned on, but the nozzle is turned off so that no water flows throughthe hose. The hose lies horizontally on the ground, and a stream of water sprays vertically out of a small leak to a height of 0.68 m. What is the pressure inside the hose?
Solution:
Chapter 15 Fluids Q.64P
A water tank springs a leak. Find the speed of water emerging from the hole if the leak is 2.7 m below the surface of the water, which is open to the atmosphere.
Solution:
Chapter 15 Fluids Q.65P
(a) Find the pressure difference on an airplane wing if air flows over the upper surface with a speed of 115 m/s, and along the bottom surface with a speed of 105 m/s. (b) If the area of the wing is 32 m2, what is the net upward force exerted on the wing?
Solution:
Chapter 15 Fluids Q.66P
On a vacation flight, you look out the window of the jet and wonder about the forces exerted on the window. Suppose the air outside the window moves with a speed of approximately 170 m/s shortly after takeoff, and that the air inside the plane is at atmospheric pressure, (a) Find the pressure difference between the inside and outside of the window, (b) If the window is 25 cm by 42 cm, find the force exerted on the window by air pressure.
Solution:
Chapter 15 Fluids Q.67P
IP During a thunderstorm, winds with a speed of 47.7 m/s blow across a flat roof with an area of 668 m2. (a) Find the magnitude of the force exerted on the roof as a result of this wind. (b) Is the force exerted on the roof in the upward or downward direction? Explain.
Solution:
Chapter 15 Fluids Q.68P
A garden hose with a diameter of 0.63 in. has water flowing in it with a speed of 0.78 m/s and a pressure of 1.2 atmospheres. At the end of the hose is a nozzle with a diameter of 0.25 in. Find (a) the speed of water in the nozzle and (b) the pressure in the nozzle.
Solution:
Chapter 15 Fluids Q.69P
IP Water flows in a cylindrical, horizontal pipe. As the pipe narrows to half its initial diameter, the pressure in the pipe changes, (a) Is the pressure in the narrow region greater than, less than, or the same as the initial pressure? Explain, (b) Calculate the change in pressure between the wide and narrow regions of the pipe. Give your answer symbolically in terms of the density of the water, p, and its initial speed v.
Solution:
Chapter 15 Fluids Q.70P
BIO Vasodilation When the body requires an increased blood flow rate in a particular organ or muscle, it can accomplish this by increasing the diameter of arterioles in that area. This is referred to as vasodilation. What percentage increase in the diameter of an arteriole is required to double the volume flow rate of blood, all other factors remaining the same?
Solution:
Chapter 15 Fluids Q.71P
BIO (a) Find the volume of blood that flows per second through the pulmonary artery described in Example 15-10. (b) If the radius of the artery is reduced by 18%, by what factor is the blood flow rate reduced? Assume that all other properties of the artery remain unchanged.
Solution:
Hence, the rate of flow is reduced by a factor of.2.2
Chapter 15 Fluids Q.72P
· BIO An Occlusion in an Artery Suppose an occlusion in an artery reduces its diameter by 15%, but the volume flow rate of blood in the artery remains the same. By what factor has th pressure drop across the length of this artery increased?
Solution:
Chapter 15 Fluids Q.73P
IP Water at 20 “C flows through a horizontal garden hose at the rate of 5.0 × 10−4 m3/s. The diameter of the garden hose is 2.5 cm. (a) What is the water speed in the hose? (b) What is the pressure drop across a 15-m length of hose? Suppose the cross-sectional area of the hose is halved, but the length and pressure drop remain the same, (c) By what factor does the waterspeed| change? (d) By what factor does the volume flow rate change? Explain,
Solution:
Chapter 15 Fluids Q.74GP
Solution:
Different water levels in the tube and in the main body of the weather glass indicate the difference in pressure between the atmosphere and inside the weather glass. As a low-pressure system approaches, atmospheric pressure drops. This allows the water level in the tube to rise.
Chapter 15 Fluids Q.75GP
CE A helium-filled balloon for a birthday party is being brought home in a car. The balloon is connected to a string, and the passenger holds the lower end of the string in her lap. When the car i s a t res t a t a stop sign the string is vertical. As the car accelerates away from the light, does the string going to the balloon lean forward, lean backward, or remain vertical?
Solution:
Solution:
If the car accelerates forward, the air inside the car shifts towards backside and so the passengers are pressed back into their seats this makes the air pressure inside the car increases from front to back. According to buoyancy the helium-filled balloon moves in the direction of decreasing pressure. Thus, the balloon moves toward the front of the car.
Chapter 15 Fluids Q.76GP
·CE Predict/Explain A person floats in a boat in a small backyard swimming pool. Inside the boat with the person are some bricks, (a) If the person drops the bricks overboard to the bottom of the pool, does the water level in the pool increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. When the bricks sink they displace less water than when they were floating in the boat; hence, the water level decreases.
II. The same mass (boat + bricks + person) is in the pool in either case, and therefore the water level remains the same.
III. The bricks displace more water when they sink to the bottom than they did when they were above the water in the boat; therefore the water level increases.
Solution:
(a)
Consider a person drops the bricks overboard to the bottom of the pool, same volume of water separated. Therefore the water levels in the pool increase.
(b)
The bricks displace more water when they sink to the bottom than they did when they were above the water in the boat. Therefore, the water level increases.
Therefore, the best explanation among the given options is (III).
Chapter 15 Fluids Q.77GP
CE A person floats in a boat in a small backyard swimming pool. Inside the boat with the person are several blocks of wood. Suppose the person now throws the blocks of wood into the pool, where they float, (a) Does the boat float higher, lower, or at the same level relative to the water? (b) Does the water level in the pool increase, decrease, or stay the same?
Solution:
Concept:
The Archimedes’s principle states that an object completely immersed in a fluid experiences an upward buoyant force equal in magnitude to the weight of fluid displaced by the object.
Solution:
(a) As the person throws the blocks of wood into the pool, the boat is carrying a reduced weight. Thus, it floats higher relative to the water.
(b) The water level in the pool remains the same because the blocks of wood displace the same amount of water as they are in water or in the boat. In both cases, they displace a volume of water with a weight equal to their weight.
Chapter 15 Fluids Q.78GP
Solution:
Chapter 15 Fluids Q.79GP
CE A pan half-filled with water is placed near the run of a rotating turntable. Is the normal to the surface of the water in the pan tilted outward away from the axis of rotation, tilted inward toward the axis of rotation, or is the water surface level and the normal vertical? (Refer to Problem 68 in Chapter 6 for a similar situation.)
Solution:
SOLUTION:
As we move farther from the axis of rotation, the water level in the pan increases. As a result, any amount of water in the pan will experience a net force directed toward the axis of rotation, as it is in a circular motion. Hence, the surface of the water in the pan is tilted inward toward the axis of rotation.
Chapter 15 Fluids Q.80GP
Solution:
Given:
Answer: It will stay where it is released.
The marble will stay where it is released because the surface of the water is perpendicular to the local effective gravity of the rotating turntable even the water itself does not flow inward or outward when it is filled at this angle.
If the water is frozen, and a marble is placed on its surface the marble will stay just as the liquid water did before it was frozen.
Chapter 15 Fluids Q.81GP
CE BIO Sphygmomanometer” When a person’s blood pressure is taken with a device known as a sphygmomanometer, it is measured on the arm, at approximately the same level as the heart. If the measurement were to be taken on the patient’s leg instead, would the reading on the sphygmomanometer be greater than, less than, or the same as when the measurement is made on the arm?
Solution:
SOLUTION:
The pressure in a fluid increases with depth. The reading of blood pressure on the sphygmomanometer when the measurement is made at the leg is greater than the measurement is made on the arm. This is due to the reason that the leg of the standing person is below the heart level (or arm).
Chapter 15 Fluids Q.82GP
At what depth below the ocean surface is the pressure equal to two atmospheres?
Solution:
Chapter 15 Fluids Q.83GP
Su ersonic Erosion In waterjet cutting, a stream of supersonic water is used to slice through materials ranging from sheets of paper to solid steel plates. The water is held ina reservoir at 59,5OÜ psi and allowed to exit througha small orifice at high speed. Find the exit speed of the water, and compare with the speed of sound.
Solution:
Chapter 15 Fluids Q.84GP
A water main broke on Lake Shore Drive inChicago on November 8, 2002, shooting water straight upward to a height of 8.0 ft. What was the pressure in the pipe?
Solution:
Chapter 15 Fluids Q.85GP
Solution:
Chapter 15 Fluids Q.86GP
BIO Power Output of the Heart The power output of the heart is given by the product of the average blood pressure, 1.33 N/cm2, and the flow rate, 105 cm3/s. (a) Find the power of the heart. Give your answer in watts, (b) How much energy does the heart expend in a day? (c) Suppose the energy found in part (b) is used to lift a 72-kg person vertically to a height h Find h, in meters.
Solution:
Chapter 15 Fluids Q.87GP
An above-ground backyard swimming pool is shaped like a large hockey puck, with a circular bottom and a vertical wall forming its perimeter. The diameter of the pool is 4.8 m and its depth is 1.8 m. Find the total outward force exerted on the vertical wall of the pool by the water, assuming the pool is completely filled.
Solution:
.
Chapter 15 Fluids Q.88GP
Asolid block is suspended from a spring scale. When the block is in air, the scale reads 35.0 N, when immersed in water the scale reads 31.1 N, and when immersed in oil the scale reads 31.8 N. (a) What is the density of the block? (b) What is the density of the oil?
Solution:
Chapter 15 Fluids Q.89GP
A wooden block with a density of 710 kg/m3 and a volume of 0.012 m3 is attached to the top of a vertical spring whose force constant is k = 540 N/m. Find the amount by which the spring is stretched or compressed if it and the wooden block are (a) in air or (b) completely immersed in water. [The density of air may be neglected in part (a).]
Solution:
Chapter 15 Fluids Q.90GP
IP Floating a Ball and Block A 1.25-kg wooden block has an iron ball of radius 1.22 cm glued to one side, (a) If the block floats in water with the iron ball “high and dry,” what is the volume of wood that is submerged? (b) If the block is now inverted, so that the iron ball is completely immersed, does the volume of wood that is submerged in water increase, decrease, or remain the same? Explain, (c) Calculate the volume of wood that is submerged when the block is in the invertedposition.
Solution:
.
Chapter 15 Fluids Q.91GP
On a bet, you try to remove water from a glass by blowing across the top of a vertical straw immersed in the water. What is the minimum speed you must give the air at the top of the straw to draw water upward through a height of 1.6 cm?
Solution:
Chapter 15 Fluids Q.92GP
The Depth of the Atmosphere Evangelista Torricelli (1608-1647) was the first to put forward the idea that we live at the bottom of an ocean of air. (a) Given the value of atmospheric pressure at the surface of the Earth, and the fact that there is zero pressure in the vacuum of space, determine the depth of the atmosphere, assuming that the density of air and the acceleration of gravity are constant, (b) According to this model, what is the atmospheric pressure at the summit of Mt. Everest, 29,035 ft above sea level. (In fact, the density of air and the acceleration of gravity decrease with altitude, so the result obtained here is less than the actual depth of the atmosphere. Still this is a reasonable first estimate.)
Solution:
Chapter 15 Fluids Q.93GP
Solution:
Chapter 15 Fluids Q.94GP
Solution:
Chapter 15 Fluids Q.95GP
IP A backyard swimming pool is circular in shape and contains water to a uniform depth of 38 cm. It is 2.3 m in diameter and is not completely filled, (a) What is the pressure at the bottom of the pool? (b) If a person gets into the pool and floats peacefully, does the pressure at the bottom of the pool increase, decrease, or stay the same? (c) Calculate the pressure at the bottom of the pool if the floating person has a mass of 72 kg.
Solution:
Chapter 15 Fluids Q.96GP
A prospector finds a solid rock composed of granite (p = 2650 kg/m3) and gold. If the volume of the rock is 3.55 × 10−4 m3, and its mass is 3.81 kg, (a) what mass of gold is contained in the rock? What percentage of the rock is gold by (b) volume and (c) mass?
Solution:
Chapter 15 Fluids Q.97GP
The Maximum Depth of the Earth’s Crust Consider the crustal rocks of the Earth to be a fluid of density 3.0 × 103 kg/m3. Under this assumption, the pressure at a depth h within the crust is P = Pat + pgh. If the greatest pressure crustal rock can sustain before crumbling is 1.2 × 103Pa, find the maximum depth of the Earth’s crust. (Below this depth the crust changes from a solid to a plasticlike material.)
Solution:
Chapter 15 Fluids Q.98GP
IP (a) If the tension in the string in Active Example 15-1 is 0.89 N, what is the volume of the wood? Assume that everything else remains the same, (b) If the string breaks and the wood floats on the surface, does the water level in the flask rise, drop, or stay the same? Explain, (c) Assuming the flask is cylindrical with a cross-sectional area of 62 cm2, find the change in water level after the string breaks.
Solution:
Chapter 15 Fluids Q.99GP
Solution:
Chapter 15 Fluids Q.100GP
A tin can is filled with water to a depth of 39 on. Ahole 11 cm above the bottom of the can produces a stream of water that directed at an angle of 36° above the horizontal. Find (a) the range and (b) the maximumheight of this stream of water
Solution:
Chapter 15 Fluids Q.101GP
BOA person weighs 685 N in air but only 497 N when standing in water up to the hips. Find (a) the volume of each of the person’s legs and (b) the mass of each leg, assuming they havea density thatis “1.05 times the density of water
Solution:
Chapter 15 Fluids Q.102GP
A horizontal pipe carries oil whose coefficient of viscosity is 0.00012 N · s/m2. The diameter of the pipe is 5.2 cm, and its length is 55 m. (a) What pressure difference is required between the ends of this pipe if the oil is to flow with an average speed of 1.2 m/s? (b) Whatis the volume flow rate in this case?
Solution:
Chapter 15 Fluids Q.103GP
BIO A patient is given an injection with a hypodermic needle 3.3 cm long and 0.26 mm in diameter. Assuming the solution being injected has the same density and viscosity as water at 20°C, find the pressure difference needed to inject the solutionat the rate of 1.5 g/s.
Solution:
=320kPa
Chapter 15 Fluids Q.104GP
An Airburst over Pennsylvania On the evening of July 23, 2001, a meteor streaked across the skies of Pennsylvania, creating a spectacular fireball beforeexploding in the atmosphere with an energy release of 3 kilotons of TNT. The pressure wave from the airburst caused an increase in pressure of 0.50 kPa, enough to shatter some windows. Find the force that this”overpressure” would exert on a 34-in. × 46-in. window. Give your answer in newtons and pounds.
Solution:
Chapter 15 Fluids Q.105GP
Going Over Like a Mythbuster Lead Balloon On one episode of Mythbusters, Jamie and Adam try to make a lead balloon that will float when filled with helium. The balloon they constructed was approximately cubical in shape, and 10 feet on a side. They used a thin lead foil, which gave the finished balloon a mass of 11 kg. (a) What was the thickness of the foil? (b) Would the lead balloon float if filled with helium? (c) If the balloon does float, what would be the most mass it could lift in addition to its own mass?
Solution:
Chapter 15 Fluids Q.106GP
IP A pan half-filled with water is placed in the back of an SUV. (a) When the SUV is driving on the freeway with a constant velocity, is the surface of the water in the pan level, tilted forward, or tilted backward? Explain, (b) Suppose the SUV accelerates in the forward direction with a constant acceleration a. Is the surface of the water tilted forward, or tilted backward? Ex-plain. (c) Show that the angle of tilt, 0, in part (b) has a magnitude given by tan 6 = a/g, where g is the acceleration of gravity.
Solution:
Solution:
(a) Since the SUV is at a constant velocity, there is no net external force with regard to the pan-SUV system, and thus, the weight and normal force cancel. The surface of the water in the pan is level.
(b)Inthlskistance,therelsacceleratlonbithe x-dlrectlonthlsleadstoawlndspeed generated over the surface of the watet The wind speed S higher at fr,) where It just meets the pan, and the speed slows down on the back end & the pan due to resistive ltrces. According to Bemouirs equation, this leads to an Increase In pressure at the back end.
Chapter 15 Fluids Q.107GP
A wooden block of cross-sectional area A, height H, and density p1 floats in a fluid of density p2. If the block is displaced downward and then released, it will oscillate with simple harmonic motion. Find the period of its motion.
Solution:
Chapter 15 Fluids Q.108GP
A round wooden log with a diameter of 73 cm floats with one-half of its radius out of the water. What is the log’s density?
Solution:
Chapter 15 Fluids Q.109GP
Solution:
Chapter 15 Fluids Q.110GP
A geode is a hollow rock with a solid shell and an air-filled interior. Suppose a particular geode weighs twice as much in air as it does when completely submerged in water. If the density of the solid part of the geode is 2500 kg/m3, what fraction of the geode’s volume is hollow?
Solution:
Chapter 15 Fluids Q.111GP
Solution:
Chapter 15 Fluids Q.112GP
Solution:
Chapter 15 Fluids Q.113GP
A hollow cubical box, 0.29 m on a side, with walls of negligible thickness floats with 35% of its volume submerged. What mass of water can be added to the box before it sinks?
Solution:
Chapter 15 Fluids Q.114PP
Solution:
Chapter 15 Fluids Q.115PP
Solution:
Chapter 15 Fluids Q.116PP
Solution:
Chapter 15 Fluids Q.117PP
Solution:
Chapter 15 Fluids Q.118IP
· · IP Referring to Example 15-4 Suppose we use a different vegetable oil that has a higher density than the one in Example 15-4. (a) If everything else remains the same, will the height difference, h, increase, decrease, or remain the same? Explain, (b) Find the height difference for an oil that has a density of 9.60 × 102 kg/m3.
Solution:
Chapter 15 Fluids Q.119IP
Referring to Example 15-4 Find the height difference, h, if the depth of the oil is increased to 7.50 cm. Assume everything else in the problem remains the same.
Solution:
Chapter 15 Fluids Q.120IP
Referring to Example 15-9 (a) Find the height H required to make D = 0.655 m. Assume everything else in the problem remains the same, (b) Find the depth h required to make D = 0.455 in. Assume everything else in the problem remains the same.
Solution:
Chapter 15 Fluids Q.121IP
Referring to Example 15-9 Suppose both h and H are increased by a factor of two. By what factor is the distance D increased?
Solution:
